related matlab program :

5. (a) Plot the heating profiles
Heating profile :
left (figure 1): contour ,
right (figure 2) : profile for each S (S=-0.5, S=0, S=0.5 left to right)
mpo663_hw2_heating_profile1.pngmpo663_hw2_heating_profile2.png
dotted line (from figure2) : the height of maximum heating occurs.

Verify that the total heat added (vertical integral) is the same in all cases.
>> sum(hprofile_n05);ans =8.8752
>> sum(hprofile_0);ans =8.8752
>> sum(hprofile_p05);ans =8.8752

5(b) Calculate the Rossby radii for the two vertical modes.
L_R1 = 466.667km (mode 1 : m1=1pi/14km)

L_R2 = 233.333 km (mode 2 : m2=2pi/14km)

5(c)
V (when L_R1 is used, figure 100) V (when L_R2 is used, Figure 101) : I used h0=1 for V calculation.
mpo663_hw2_v1.pngmpo663_hw2_v2.png

5(c) Contour the tangential (v) wind
Tangential wind when S=-0.5 (below, figure 8) : shallow convection fraction
dotted line : the height where maximum heating occurs (in figure 2)
mpo663_hw2_tangential_wind_s_n05.png

Tangential wind (S=0) : below (figure 9)
mpo663_hw2_tangential_wind_s0.png

Tangential wind (S=0.5) : below Figure 10 : Stratiform fraction
mpo663_hw2_tangential_wind_s_p05.png

5 (d) Plot the domain-integrated KE versus S for values of S in [-0.5,0.5]. Is the curve nonlinear? yes, it's nonlinear. KE ~ v^2

mpo663_hw2_figure11.png
5(e) Surface fluxes are approximately proportional to surface wind speed. Plot the domain-averaged surface wind speed versus S for values of S in [-0.5,0.5]. Is the curve nonlinear? Discuss the implications for tropical cyclogenesis, in terms of convective heating profiles and their dependence on low-level rain evaporation and downdrafts.
mpo663_hw2_figure12_small.png